The gains of phase-locked-loop (PLL) have significant impacts on the power transfer limits for the voltage source converter (VSC)\nconnected to weak AC system. Therefore, in this paper, an improved PLL control, respectively, with alternative damping factors for\nrectifier and inverter is proposed. First, it is proved that the impedance angle of AC system has a great impact on the small-signal\nstability of the VSC system.With the same variation tendency ofTh�´evenin equivalent resistance, the limits of power transmission\nare changing in opposite trends for rectifier and inverter. Second, the improved PLL with alternative damping factors is proposed\nbased on the participation factor analysis. Third, the optimal damping factors of the improved PLL control for rectifier and inverter\nare calculated. Simulations and calculations validated the following three conclusions: (1) in rectifying operation, the equivalent\nsystem resistance has a negative impact on the stability of the system and this is not the case for inverting operation; (2) adding\nthe alternative damping factors to PLL control shows similar results compared with changing the impedance angle of AC system;\n(3) the proposed optimal damping factors of PLL can effectively extend the power transfer limits under both rectifier and inverter\nmodes.
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